Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 3 starting from 10. Rule 2: Subtract 7 starting from 58. What is the first term that appears in both sequences? (2 points) a 30 b 55 c 60 d 180

The quotient of the expression 5x^2/7÷10x^3/21 is 3/(2x)

From the question, we have the following parameters that can be used in our computation:

5x^2/7÷10x^3/21

Assume that no denominator has a value of 0, we have

5x^2/7÷10x^3/21 = 5x^2/7 ÷ 10x^3/(7 * 3)

Express as products

So, we have the following representation

5x^2/7÷10x^3/21 = 5x^2/7 * (7 * 3)/10x^3

When the factors are evaluated, we have

5x^2/7÷10x^3/21 = 5 * 3/10x

So, we have

5x^2/7÷10x^3/21 = 15/10x

This gives

5x^2/7÷10x^3/21 = 3/(2x)

Hence, the solution is 3/(2x)

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Step-by-step explanation:

Perimeter =  2 m + 2 * 7m

Perimeter = 2 ( m + 7m)

Perimeter = 2m + 14m

Perimeter = 16 m                          Pick any of them

Answer:

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $100, r = 9% = 0.09, n = 1 (compounded annually), and t = 16. We want to find A.

A = 100(1 + 0.09/1)^(1*16)

A = $397.42

Therefore, Javae will have $397.42 in his account on his 30th birthday. The answer is option D.

The solution for the value of x is 55.

Since the segments of the secant segment and the tangent segment share an endpoint outside of the circle.

According to Tangent-Secant Theorem, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. That is:

x² = 5 * (5 + 6)

x = 5 * 11

x = 55

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Answer:

  181.875 cm³

Step-by-step explanation:

You want to know the amount of additional material Jessica needs to make a prism with a volume of 35 cm³ and one that is dilated by a factor of 2.5, given that she has 400 cm³ of material.

The dilation factor for volume is the cube of the linear dilation factor:

  2.5³ = 15.625

so the volume of the scaled-up prism will be ...

  (35 cm³) × 15.625 = 546.875 cm³

The total volume of material Jessica needs for the two prisms is ...

  35 cm³ + 546.875 cm³ = 581.875 cm³

Since Jessica has 400 cm³ of material, the amount she needs is ...

  581.875 cm³ - 400 cm³ = 181.875 cm³

Jessica needs 181.875 cm³ more material to make the second prism.

The amount of cookie each sister receives is A = 1/12

Given data ,

Let the amount of cookie each sister receives be A

Now , the equation is

If Jessica ate a part of the cookie and had 1/4 remaining, then she ate 3/4 of the original cookie

Since she wants to give the remaining 1/4 of the cookie to her three sisters to share equally, each sister will receive 1/3 of that 1/4

To find the fraction of the original cookie that each sister will receive, we need to multiply the fraction received by the fraction of the cookie that is left

(1/3) x (1/4) = 1/12

Hence , each sister will receive 1/12 of the original cookie to eat

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Answer:

The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Step-by-step explanation:

To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.

Next, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.

Substituting these values into the formula, we get:

x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)

Simplifying:

x = (4 ± sqrt(176)) / 2

x = (4 ± 4sqrt(11)) / 2

x = 2 ± 2sqrt(11)

Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).

Answer:

[tex]0.42[/tex]÷[tex]7[/tex]

Step-by-step explanation:

First, let's count the number of colored squares in the hundredth-grid.

There are a total of 42 hundredth-squares.

Since this is measured in hundredths, the number it represents is 0.42.

Each of the different colors represents a separate group that 0.42 is being divided into. There are 7 separate groups.

Since 0.42 is being divided into 7 groups, the equation that is being represented is:

[tex]0.42[/tex]÷[tex]7[/tex]

The coordinates for the dilated figure would be A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2).

The kind of dilation that was done is called a reduction.

When you dilate a figure with a scale factor k = 1/3, you are performing a reduction, because the scale factor is between 0 and 1. In this case, the dilation will shrink the original figure by a factor of 1/3.

To find the coordinates of the dilated points, multiply the x and y coordinates of each point by the scale factor (1/3):

A' = (-6 x 1/3, 6 x 1/3) = (-2, 2)

B' = (-6 x 1/3, -3 x 1/3) = (-2, -1)

C' = (6 x 1/3, -3 x 1/3) = (2, -1)

D' = (6 x 1/3, 6 x 1/3) = (2, 2)

The coordinates of the dilated figure are A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2). This type of dilation is a reduction, as the figure becomes smaller.

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The slope of the function f(x) = -3x^2 +11 at any value of x is given by 6x.

The definition of derivative is given by the limit as h approaches 0 of [f(a+h) - f(a)] / h,

where f(x) is a function and a is a fixed value of x.

To find the slope of the function[tex]f(x) = -3x^2 +11[/tex]  at any value of x, we need to use this definition of derivative.
So, let's plug in f(x) = -3x^2 +11 and a = x into the formula.

This gives us:
lim as h approaches 0 of [tex][-3(x+h)^2 + 11 - (-3x^2 + 11)] / h[/tex]
Simplifying this expression, we get:
lim as h approaches 0 of [tex][-3x^2 - 6hx - 3h^2 + 11 + 3x^2 - 11] / h[/tex]
Combining like terms, we get:
lim as h approaches 0 of [tex][-6hx - 3h^2] / h][/tex]
Factoring out an h from the numerator, we get:
lim as h approaches 0 of [-h(6x + 3h)] / h
Canceling out the h in the numerator and denominator, we get:
lim as h approaches 0 of 6x + 3h
Now, we can plug in h = 0 to find the slope of the function at any value of x:
6x + 3(0) = 6x.

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The best graphical representation to display the data on the GPA of 318 students at East River High School would be a histogram.

A histogram is a graphical representation of data that groups data into bins or intervals and displays the frequency of occurrences of data within each bin. In this case, the bins would represent GPA ranges, and the frequency would represent the number of students falling within each GPA range.

A histogram is a good choice for displaying this data because it allows the viewer to see the distribution of GPA scores across the student population. It provides a visual representation of how many students fall within certain GPA ranges and can help identify trends in the data.

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The simplified ratio is 3 light bulbs for every 1 chandelier.

It should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.

In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:

9 light bulbs ÷ 3 = 3 light bulbs

3 chandeliers ÷ 3 = 1 chandelier

So the simplified ratio is 3 light bulbs for every 1 chandelier.

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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.

De acuerdo a la información, el área total de la placa es de 10800 centímetros cúbicos.

El área que debe cubrir la placa es un área en forma de rectángulo. Por está razón, el área que se va a cubrir puede ser calculada utilizando la siguiente formula:

Área = largo x altura

De acuerdo a lo anterior, encontremos el área reemplazando los valores correspondientes:

60 cm x 180 cm = 10800 centímetros cúbicos

Por lo tanto, el área de la zona a cubrir por la placa es de  10800 centímetros cúbicos.

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Answer:

(C) and (D) are correct.

Therefore, expression 3x5/6 simplifies to 3 5/6.

In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables. Expressions can be evaluated, simplified, and manipulated using mathematical rules and operations to obtain new expressions or values.

Here,

To simplify 3x5/6, we can rewrite it as (3/1) × (5/6). Multiplying the numerators and denominators, we get:

(3/1) × (5/6) = 15/6

= 2 3/6

Since 3/6 can be simplified to 1/2, we have:

2 3/6 = 2 1/2

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The measure of side ‘b’ in the given triangle ABC, with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11 is option-c:12.516, which is found using Sine-law.

In a scalene or oblique triangle (a non-right triangle), the law of sine describes the relationship between the sides and angles. Trigonometric laws such as the law of sines and law of cosines are crucial when "solving a triangle" by calculating the unknown angles or sides. The ratio of a triangle's side lengths to the sine of each of its opposite angles must be equal in order for the sine rule to apply. Triangle side length ratios to their corresponding opposite angles are connected by the law of sines. All three sides and the diagonal angles maintain the same ratio.

Given that ∠A= 54° ,∠C= 59° & side BC=a=11

We know that ∠A + ∠B + ∠C = 180°   {angle sum property}

Consider △ABC,

54° + 59° +  ∠B = 180°

113° +  ∠B = 180°

∠B = 180°- 113°

∠B = 67°

Applying Sine-Law,

[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B} = \frac{C}{sin\ C}[/tex]

By using,

[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B}[/tex] , we get:

[tex]\frac{11}{sin\ 54} =\frac{B}{sin\ 67}\\ \\\frac{11}{0.80901} =\frac{B}{0.92050} \\\\B=\frac{11}{0.80901} \times 0.92050[/tex]

B = 13.59686 x 0.92050

B = 12.5159

B = 12.516

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Refer to the attachment for the complete question.

The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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The exponential function f(x) = 2^x is given by the blue graph on the given graph.

The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function in this problem is defined as follows:

y = 2^x.

Two relevant numeric values are given as follows:

Hence the function is represented by the blue graph.

The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.

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Answer:

67 [tex]ft^{2}[/tex]

Step-by-step explanation:

Divide the shape into more recognizable shapes.
5*7 = 35
7*4 = 28
35+28
67

The solution to the linear equation is determined as 5.

The equation to solve is:

3x - 8 = 7

To solve for x, you can follow these steps:

Step 1: Add 8 to both sides of the equation to isolate the term with x on one side:

3x - 8 + 8 = 7 + 8 (combine constants here)

This simplifies to:

3x = 15

Step 2: Divide both sides of the equation by 3 to solve for x:

3x/3 = 15/3

This simplifies to:

x = 5

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Answer: Width: 12 Height: 24 Depth: 18

Step-by-step explanation: Width= 12, 12x2=24 and 12x1.5=18. 12x24x18=5184in3

Answer:

B. It is not a function.

This graph is a circle.

The true statement regarding the hypothesis will be:

The correct option is D II and III only.

A two-sample t-test of the hypotheses Hoμ1-2 = 0 versus H 41-μ2> 0 produces a p-value of 0.03.

In this case, a 95 percent confidence interval for the difference in means will contain the value 0.

Also, a 99 percent confidence interval for the difference in means will contain the value 0.

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Answer:

First image.

Step-by-step explanation:

Second image.

From the similar triangle, y=8.7, and x=4

From the similar triangle,

First lets find the angle both triangles share

to determine the value , solving on the bigger triangle,

cosθ= adjacent/hypothenus

cosθ= 5/10

cosθ= 0.5

θ= 60

Therefore, to obtain y,

sin 60= y/10

y=10 sin 60

y=8.7

from the smaller triangle,

to determine x

cos 60=2/x

x cos 60=2

x=2/cos60

x= 4.

Therefore, y=8.7, and x=4.

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The volume of the other solid (Solid B) is 3456 cubic feet.

Solid A has edges of 4 feet, and its volume is given as 16 cubic feet. Solid B has edges of 24 feet.

Since the solids are similar, they have the same shape, and their corresponding lengths are proportional. To find the ratio of their corresponding lengths, we can divide the length of an edge of Solid B by the length of an edge of Solid A:

Ratio = (length of edge of Solid B) / (length of edge of Solid A)

Ratio = 24 feet / 4 feet

Ratio = 6

Now that we have the ratio of their corresponding lengths, we can find the ratio of their volumes. The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths:

Volume ratio = (length ratio)³

Volume ratio = 6³

Volume ratio = 216

Now we can use the volume ratio to find the volume of Solid B:

Volume of Solid B = (Volume of Solid A) × (Volume ratio)

Volume of Solid B = 16 ft³ × 216

Volume of Solid B = 3456 ft³

So, the volume of the other solid (Solid B) is 3456 cubic feet.

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The requreid volume of the right cone is 1,411.2 cubic units.

We need to use the formula for the volume of a cone:
[tex]V = (1/3)\pi r^2h[/tex],

where r is the radius of the base of the cone and h is the height of the cone.We are given that the height of the cone is 21 and the radius of the base is 8.

V = (1/3)π(8²)(21)
V = 1,411.2 cubic units (rounded to the nearest tenth).

Therefore, the volume of the right cone is approximately 1,411.2 cubic units.

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Taking the quotient between the total volume and the flow rate, we can see that the correct option is D.

We know that water flows at a rate of 1.5*10^4 gallons per second. We know that 6.525*10^6 gallons flowed while Jeremy was watching, then the time that he has been watching is the quotient between these values, we will get:

time = ( 6.525*10^6)/(1.510^4) seconds =  (652.5/1.5) second = 435 seconds

We know that 60 secons = 1 minute, then:

435/60  = 7 + 15/60

So he has been watching for 7 minutes and 15 seconds, the correct option is D.

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The dimensions of the rectangle are either 25" by 8" or 20" by 10".

The perimeter of a two-dimensional shape is the space surrounding it. It is calculated using length units like inches or metres. The lengths of all the sides of a rectangle are added up to determine its perimeter.

Area is a unit used to describe how much room there is inside a two-dimensional form. It is calculated using area units like square inches or square metres. A rectangle's area is calculated by multiplying its length by its width.

The perimeter of the rectangle is given as:

Perimeter = 2(length + width)

Substituting the value we have:

90 = 2(L + W)

45 = L + W

Now, the area is given as:

Area = length × width

Substituting the values we have:

200 = L × W

The above equation can be written as:

W = 200/L

Substituting the value of W in the first equation we have:

45 = L + 200/L

45L = L² + 200

L² - 45L + 200 = 0

L = (45 ± √(45² - 4×1×200)) / (2×1)

L = (45 ± 5) / 2

L = 25 or L = 20

Now, for L = 25 the value of W is:

W = 200 / 25 = 8

For L = 20:

W = 200 / 20 = 10

Hence, the dimensions of the rectangle are either 25" by 8" or 20" by 10".

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